Use the Empirical Rule to Solve the Problem Note: the Sample Mean and Sample Standard Deviation of These

question 90

Multiple Choice

Use the empirical rule to solve the problem.
-The weights, in kilograms, of 60 randomly selected female school children from Country A, ages 12-15 years old, are presented in increasing order in the following table: $$\begin{array} { l l l l l l l l l } 35.3 & 37.6 & 38.1 & 38.8 & 38.9 & 39.0 & 39.1 & 40.2 & 41.2 \\41.2 & 41.3 & 41.7 & 42.1 & 42.1 & 42.1 & 42.3 & 42.6 & 42.7 \\42.8 & 43.2 & 43.3 & 43.3 & 44.1 & 44.3 & 44.5 & 44.8 & 45.1 \\45.1 & 45.2 & 45.4 & 45.4 & 45.6 & 45.8 & 45.8 & 46.0 & 46.2 \\46.3 & 46.6 & 46.6 & 47.1 & 47.3 & 47.5 & 47.6 & 47.7 & 48.1 \\48.1 & 48.3 & 48.3 & 48.4 & 48.6 & 48.6 & 48.8 & 49.0 & 49.6 \\50.3 & 51.0 & 51.9 & 52.9 & 52.9 & 57.4 & & &\end{array}$$ Note: The sample mean and sample standard deviation of these weights are, respectively, 45.19 and 4.19.

• A)(i)Use the Empirical rule to estimate the percentages of the observations that lie within 1standard
• Deviation(s)to either side of the mean.
• (ii)Use the data to obtain the exact percentages of the observations that lie within 1standard
• Deviation(s)to either side of the mean. (i)Assuming that the weights have a roughly bell-shaped distribution, approximately 63% of the observations should lie within 4.19 kg of the mean 45.19, or within the interval from 40.5 to 49.68;
• (ii)45 of the 60 observations (75%)lie between 40.5 to 49.68.
• B)(i)Assuming that the weights have a roughly bell-shaped distribution, approximately 68% of the observations should lie within 4.19 kg of the mean 45.19, or within the interval from 39.7 to 50.48;
• (ii)43 of the 60 observations 71.67% lie between 39.7 to 50.48.
• C)(i)Assuming that the weights have a roughly bell-shaped distribution, approximately 63% of the observations should lie within 4.19 kg of the mean 45.19, or within the interval from 41 To 49.38;
• (ii)40 of the 60 observations 66.67% lie between 41 and 49.38.
• D)(i)Assuming that the weights have a roughly bell-shaped distribution, approximately 68% of the observations should lie within 4.19 kg of the mean 45.19 or within the interval from 41 To 49.38;
• (ii)45 of the 60 observations (75%)lie between 41 and 49.38.

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